Reputations in Repeated Games

A lecture by Visiting Scholar Larry Samuelson

February 13–27, 2013

5:15pm 7:15pm

Rosenwald Hall

The two-part lecture series by Larry Samuelson will examine studies of reputations built around models of repeated games.

The adverse selection approach to reputations considers games of incomplete information. The motivation for the model typically stems from a game of complete information in which the players are “normal,” and the game of incomplete information is viewed as a perturbation of the complete-information game. In keeping with this motivation, attention is typically focused on games of “nearly” complete information, in the sense that a player whose type is unknown is very likely (but not quite certain) to be a normal type. For example, a player in a repeated game might be almost certain to have stage-game payoffs given by the prisoners’ dilemma, but may with some small possibility have no other option that to play tit-for-tat.

The idea that a player has an incentive to build, maintain, or milk his reputation is then captured by the incentive that player has to manipulate the beliefs of other players about his type. Reputations exploit the updating of these beliefs to establish links between past behavior and expectations of future behavior. We say “reputations effects” arise if these links give rise to restrictions on equilibrium payoffs or behavior that do not arise in the underlying game of complete information.

The basic results identify circumstances in which reputation effects necessarily arise, imposing bounds on equilibrium payoffs that are in many cases quite striking. In some cases these reputation effects can lead to relatively high lower bounds on the payoff of the reputation builder, and to a set of equilibrium payoffs considerably smaller than the set of equilibrium payoffs of the underlying game of complete information. In other cases, the result can be equilibrium payoffs that are unfeasible in the complete-information game.

February 13, 2013 - 5:15pm February 27, 2013 - 7:15pm